On L1-Norm Based Fuzzy c-Means Clustering with Penalty Term

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  • Miyamoto Tomoaki
    Graduate School of Systems and Information Engineering, University of Tsukuba
  • Endo Yasunori
    Department of Risk Engineering, Faculty of Systems and Information Engineering, University of Tsukuba
  • Hamasuna Yukihiro
    Graduate School of Systems and Information Engineering, University of Tsukuba Research Fellow of the Japan Society for the Promotion of Science
  • Miyamoto Sadaaki
    Department of Risk Engineering, Faculty of Systems and Information Engineering, University of Tsukuba

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Other Title
  • L1ノルムを用いたペナルティ項を持つファジィc-平均法
  • L ₁ ノルム オ モチイタ ペナルティコウ オ モツ ファジィ c-ヘイキンホウ

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Abstract

Clustering is one of the unsupervised classification and fuzzy c-means (FCM) is one of the typical technique of fuzzy clustering. Endo et al. have introduced the concept of tolerance and constracted the algorithm of FCM for data with tolerance (FCM-T) to handle uncertainties with data. In the algorithm, the constraints for tolerance vectors are used. In this paper, we will try to get rid of the constraints by introducing the penalty term instead of there. On the other hand, the dissimilarity of FCM is defined as the squared L2-norm. Moreover, L1-norm based methods are also constructed. L1-norm methods can calculate results rapidly. In this paper, we will consider L1-norm based FCM.

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